Blends: a curved seam where the edge chain runs on holds the contact on itself (#1291)

A round or chamfer whose edge chain runs on across a curved seam (the end circle of a lofted tube whose axis bends) is now built: the section solve keeps its contact on the seam through a plane taken afresh at the seam's nearest point at each step. Straight seams are unchanged. Robustness seed 41 is re-recorded: its second fillet, refused before, now builds. Fixes #1213.

Co-authored-by: gvocale <gvocale@users.noreply.github.com>

crates/kernel/src/curveblend.rs

@@ -421,6 +421,29 @@ struct Section {
     q2: Vec3,
 }
 
+/// The third condition of a section's solve, in place of staying in the plane square to the edge: a contact held at a seam.
+#[derive(Clone, Copy)]
+enum Extra<'a> {
+    /// Side `k`'s contact lies in this plane (a point on it, its normal): beside a straight seam.
+    Plane(usize, Vec3, Vec3),
+    /// Side `k`'s contact lies on this curved seam (a lofted wall's seam between its two halves).
+    Seam(usize, &'a mt::Edge),
+}
+
+/// The seam's point nearest `x` and its unit tangent there.
+fn nearest_on_seam(seam: &mt::Edge, x: Vec3) -> Option<(Vec3, Vec3)> {
+    use mt::{BoundedCurve, ParametricCurve, SearchNearestParameter};
+    let curve = seam.curve();
+    let (lo, hi) = curve.range_tuple();
+    let at = |t: f64| from_p3(curve.subs(t));
+    // The nearest of a few samples starts the search: a long seam holds the point's neighbourhood
+    // far from its ends.
+    let hint = (0..=64).map(|i| lo + (hi - lo) * i as f64 / 64.0).min_by(|a, b| at(*a).dist(x).total_cmp(&at(*b).dist(x)))?;
+    let t = curve.search_nearest_parameter(p3(x), hint, 100)?.clamp(lo, hi);
+    let d = curve.der(t);
+    Some((at(t), Vec3::new(d.x, d.y, d.z).normalized()?))
+}
+
 /// Nearest point of a face's surface and the outward normal there.
 pub(crate) fn project(f: &mt::Face, p: Vec3, hint: Option<(f64, f64)>) -> Option<(Vec3, Vec3, (f64, f64))> {
     use mt::{ParametricSurface, ParametricSurface3D, SearchNearestParameter};
@@ -449,22 +472,12 @@ fn in_range(f: &mt::Face, uv: (f64, f64)) -> bool {
 }
 
 /// Solve for the ball touching both sides near `p`. `extra` adds a third condition (a plane the
-/// side-k contact must lie in); without it the centre stays in the plane through `p` square to
-/// `t`. `sigma` is +1 when the ball sits outside the material (concave edge), −1 inside.
+/// side-k contact must lie in, or a curved seam it must lie on); without it the centre stays in the
+/// plane through `p` square to `t`. `sigma` is +1 when the ball sits outside the material (concave edge), −1 inside.
 /// `cusp` is ±1 at a knife edge (the faces' normals opposite: both leave the edge the same way,
 /// along `cusp · n1 × t`, and the ball lies where the cusp has opened to its width), else 0.
 #[allow(clippy::too_many_arguments)]
-fn solve(
-    f1: &[&mt::Face],
-    f2: &[&mt::Face],
-    p: Vec3,
-    t: Vec3,
-    r: f64,
-    sigma: f64,
-    cusp: f64,
-    extra: Option<(usize, Vec3, Vec3)>,
-    tol: f64,
-) -> Option<Section> {
+fn solve(f1: &[&mt::Face], f2: &[&mt::Face], p: Vec3, t: Vec3, r: f64, sigma: f64, cusp: f64, extra: Option<Extra<'_>>, tol: f64) -> Option<Section> {
     solve_from(f1, f2, p, t, r, sigma, cusp, extra, tol, None)
 }
 
@@ -479,7 +492,7 @@ fn solve_from(
     r: f64,
     sigma: f64,
     cusp: f64,
-    extra: Option<(usize, Vec3, Vec3)>,
+    extra: Option<Extra<'_>>,
     tol: f64,
     start: Option<Vec3>,
 ) -> Option<Section> {
@@ -558,10 +571,19 @@ fn solve_from(
         // Third row: stay in the section plane, or put a contact on the seam plane.
         let (row3, g3) = match extra {
             None => (t, (c - p).dot(t)),
-            Some((k, o, m)) => {
+            Some(Extra::Plane(k, o, m)) => {
                 let q = if k == 1 { q1 } else { q2 };
                 (m, (q - o).dot(m))
             }
+            Some(Extra::Seam(k, seam)) => {
+                // The plane through the seam's nearest point to the contact, square to that side's
+                // surface, taken afresh each step: it holds the contact on the curved seam as the
+                // steps close in.
+                let (q, n) = if k == 1 { (q1, n1) } else { (q2, n2) };
+                let (on_seam, d) = nearest_on_seam(seam, q)?;
+                let m = d.cross(n).normalized()?;
+                (m, (q - on_seam).dot(m))
+            }
         };
         let a = [[n1.x, n1.y, n1.z], [n2.x, n2.y, n2.z], [row3.x, row3.y, row3.z]];
         let b = [-g1, -g2, -g3];
@@ -1126,15 +1148,16 @@ fn curve_blend_with_limit(solid: &Solid, ids: &[mt::EdgeID], size: f64, r: f64,
                 slanted.push((k, fi, p, t, None));
             }
         }
-        let extra = match here.first().cloned().filter(|_| !at_end) {
+        let extra = match here.first().filter(|_| !at_end) {
             None => None,
+            // A curved seam holds the contact on itself (the chain runs on smoothly across it: a
+            // lofted wall's two halves).
+            Some((side, seam)) if !straight(seam, tol * 10.0) => Some(Extra::Seam(*side, seam)),
             Some((side, seam)) => {
+                let side = *side;
                 // The plane through the seam square to that side's surface.
                 let o = from_p3(seam.front().point());
                 let d = (from_p3(seam.back().point()) - o).normalized().ok_or_else(|| KernelError::Failed("seam".into()))?;
-                if !straight(&seam, tol * 10.0) {
-                    return Err(unsupported("a curved seam where the edge chain turns"));
-                }
                 let fs = if side == 1 { &s1 } else { &s2 };
                 // The side's normal at the joint: from its face nearest the joint (any face of a
                 // longer side is no guide here).
@@ -1144,7 +1167,7 @@ fn curve_blend_with_limit(solid: &Solid, ids: &[mt::EdgeID], size: f64, r: f64,
                     .min_by(|a, b| a.0.dist(p).total_cmp(&b.0.dist(p)))
                     .map(|x| x.1)
                     .ok_or_else(|| KernelError::Failed("seam normal".into()))?;
-                Some((side, o, d.cross(nn).normalized().ok_or_else(|| KernelError::Failed("seam plane".into()))?))
+                Some(Extra::Plane(side, o, d.cross(nn).normalized().ok_or_else(|| KernelError::Failed("seam plane".into()))?))
             }
         };
         // On the faces of the edge from this vertex alone (the last edge's at an open chain's